2024-03-29T07:18:14Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698642022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Initial values for the Navier-Stokes equations in spaces with weights in timeFarwig, ReinhardGIGA, YOSHIKAZUHsu, Pen-YuanInstationary Navier-Stokes systeminitial valueslocal strong solutionsweighted Serrin conditionwell-chosen weak solutionsrestricted Serrin's uniquenesss theorem410We consider the nonstationary Navier-Stokes system in a smooth bounded domain R3 with initial value u0 2 L2 ( ). It is an important question to determine the optimal initial value condition in order to prove the existence of a unique local strong solution satisfying Serrin's condition. In this paper, we introduce a weighted Serrin condition that yields a necessary and su cient initial value condition to guarantee the existence of R local strong solutions u( ) contained in the weighted Serrin class T 0 ( ku( )kq)s d < 1 with 2 s + 3 q = 1 2 , 0 < < 1 2 . Moreover, we prove a restricted weak-strong uniqueness theorem in this Serrin class.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69864info:doi/10.14943/84204https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69864/1/pre1060.pdfHokkaido University Preprint Series in Mathematics10601162014-08-25engpublisher